SHANGHAI—Chinese banks are taking on new risks as they scramble to lure savers, turning a previously obscure line of business into a $1 trillion industry.

The explosion marks the latest effort by lenders to circumvent Beijing’s campaign against financial risk, and to head off rising competition from the lightly regulated shadow-banking sector and upstart high-tech rivals such as Ant Financial. It also reflects an old struggle in a country where banks can’t freely set their own interest rates.